Frame synchronization is important in digital communications. Heretofore, various approaches have been proposed to conduct frame synchronization. Specifically in orthogonal frequency division multiplexing (OFDM) systems, a conventional correlation method appends cyclic periodic training sequences at the start of the data frame at the transmitter and, at the receiver, the periodicity of the signals within an observation window is explored to obtain frame synchronization. In IEEE 802.11a and IEEE 802.16g standards, for example, the preambles contain two (or more) identical sync words of M symbols. Only M complex multiplications are needed for each timing estimate. However, when the timing offset is less than M samples (M is the period of the training sequence), the frame synchronization metric is not narrow around its peak that corresponds to the correct timing start. When the signal-to-noise ratio (SNR) is not high enough, the probability of coarse synchronization error (timing estimate errors within the length of the training sequence) is high.
A number of techniques have been proposed to sharpen the timing metric and thus reduce the variance of the timing estimation error. For example, a different sync words have been used to minimize coarse timing synchronization errors, specifically in OFDM. In a double correlation technique for MPSK systems, the nonlinear Bessel function is approximated by a second order power series, resulted in estimate which approaches the maximum likelihood (ML) solution of the frame start in the presence of the frequency offset. The complexity of this method, however, is high, requiring about M2 complex multiplications for each timing estimate. Other frame synchronization techniques have been proposed. However, prior systems and methods fail to show or suggest a permuted sequences combination for frame synchronization such as described in the present application.